The Farey series ℱn of order n, named after John Farey, is the set of fractions h/k, where h and k are integers, 0 ≤ h ≤ k ≤ n, and (h, k) = 1, in ascending order. We include 0 and 1 in the forms 0/1 and 1/1, respectively. For instance, the Farey series of order 4 is
Exercises deal with Farey series.
Show that if a/b, c/d, and e/f are successive terms of a Farey series, then
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